Emuva ngo-1887, isazi sefiziksi saseScotland uWilliam Thomson saphakamisa imodeli yakhe yejiyomethri yesakhiwo se-ether, okwakucatshangwa ukuthi iyindawo egcwele yonke indawo, ukundindizela okuzibonakalisa kithi njengamaza kagesi, kuhlanganise nokukhanya. Naphezu kokuhluleka okuphelele kwe-ether theory, imodeli yejometri yaqhubeka ikhona, futhi ngo-1993, uDenis Ware noRobert Phelan bahlongoza imodeli ethuthuke kakhulu yesakhiwo esikwazi ukugcwalisa isikhala ngangokunokwenzeka. Kusukela ngaleso sikhathi, lo modeli uye waba nesithakazelo ikakhulukazi kwizibalo noma abaculi, kodwa ucwaningo lwakamuva lubonise ukuthi lungenza isisekelo sobuchwepheshe besikhathi esizayo obusebenzisa ukukhanya esikhundleni sikagesi. Iyini igwebu le-Ware-Phelan, yini elenza lingajwayelekile, futhi lingasetshenziswa kanjani ukubamba ukukhanya? Sizothola izimpendulo zale mibuzo neminye embikweni weqembu locwaningo. Hamba.
Isisekelo socwaningo
Empeleni eminyakeni eyikhulu edlule emphakathini wesayensi kwakukhona inkolelo-mbono ethakazelisa kakhulu mayelana nendaba ethile yazo zonke izinto ezizungezile. Lo mbono wawuhloselwe ukuchaza uhlobo lwamagagasi kagesi. Kwakukholelwa ukuthi i-ether izungeza yonke into futhi iwumthombo wala magagasi. Okutholwe yisayensi okwalandela ithiyori ye-ether kwayiqeda ngokuphelele.
UWilliam Thomson
Nokho, ngo-1887, lapho inkolelo-mbono ye-ether igcwele amandla nokuthandwa, ososayensi abaningi baveza imibono yabo mayelana nokuthi i-ether ingagcwalisa kanjani yonke indawo. UWilliam Thomson, owaziwa nangokuthi uLord Kelvin, naye wayefana. Wayefuna isakhiwo esizovala isikhala ukuze kungabi nezindawo ezingenalutho. Lokhu kusesha kamuva kwabizwa ngokuthi inkinga kaKelvin.
Isibonelo sakudala: cabanga ngebhokisi eliqukethe amathini e-cola. Phakathi kwabo, ngenxa yesimo se-cylindrical, i-voids iphakama, i.e. indawo engasetshenzisiwe.
U-Thomson, ngaphezu kokukholelwa ukuthi uMhlaba wawungekho ngaphezu kweminyaka eyizigidi ezingu-40, uhlongoze isakhiwo esisha sejometri, esathuthukiswa nguDenis Ware noRobert Phelan, ngenxa yalokho saqanjwa ngabo.
Isakhiwo se-Ware-Phelan sisekelwe phezu kwekhekheba lezinyosi eligcwalisa isikhala nge-polyhedra engahlangani, engashiyi ndawo engenalutho. Ikhekheba lezinyosi, esivame ukucabanga ngalo njengama-hexagon ngenxa yekhekhe lezinyosi, empeleni liza ngezindlela eziningi ezahlukene. Kukhona i-cubic, i-octahedral, i-tetrahedral, i-rhombic dodecahedral, njll.
Isakhiwo se-Ware-Phelan
Into engavamile ngamakhekheba oju e-Ware-Phelan ukuthi aqukethe ubujamo bejometri nezakhi ezahlukene. Emgogodleni wayo, iyigwebu elikahle lamabhamuza anosayizi olinganayo.
Idlozi laleligwebu yilo elaphakanyiswa nguLord Kelvin, esilijwayele. Nokho, inguqulo yakhe yayihlanganisa amakhekheba oju afushanisiwe ayi-cubic. Isakhiwo se-Kelvin kwakuyikhekheba lezinyosi elifana ne-convex elakhiwe i-octahedron encishisiwe, eyi-polyhedron enobuso obune, egcwalisa isikhala (i-tetradecahedron), enobuso obuyisikwele obuyisi-6 kanye nobuso obuyi-hex obuyisi-8.
Le nketho yokwandisa ukugcwaliswa kwesikhala yayibhekwa njengenhle cishe iminyaka eyikhulu, kwaze kwaba yilapho u-Ware noPhelan bevula isakhiwo sabo ngo-1993.
I-Pentagondodecahedron ne-decahedron
Umehluko omkhulu phakathi kwekhekheba lezinyosi le-Ware-Phelan kanye nomanduleli walo ukusetshenziswa kwezinhlobo ezimbili zezinto ezihlanganisiwe, okuthi, nokho, zibe nevolumu efanayo: i-pentagondodecahedron (i-dodecahedron eno-tetrahedral symmetry) kanye ne-14hedron enokulinganisa okujikelezayo.
Emsebenzini esiwucabangelayo namuhla, ososayensi basePrinceton University banqume ukusebenzisa igwebu le-Ware-Phelan ezithombeni. Okokuqala, kwakudingeka ukuthola ukuthi amagwebu anjalo anezikhala ze-photonic band (PBGs), ezivimbela ukusakazeka kokukhanya kuzo zonke izinkomba kanye nawo wonke ama-polarizations phezu kwamafrikhwensi amaningi.
Ocwaningweni lwabo, ososayensi bakhombise ukuthi inethiwekhi yezithombe ze-16,9D esekwe kugwebu le-Ware-Phelan iholela ku-PBG ebalulekile (XNUMX%) enezinga eliphezulu isotropy*, okuyindawo ebalulekile yamasekhethi ezithombe.
I-Isotropy* - izici ezibonakalayo ezifanayo kuzo zonke izinhlangothi.
Igwebu le-Kelvin kanye negwebu le-C15 nazo zenze kahle ngokwe-PBG, kodwa zazingaphansi kwesakhiwo se-Ware-Phelan mayelana nalokhu.
Izifundo ezifanayo zenziwe ngaphambilini, kodwa zigxile kugwebu elomile elinezinhlangothi ezimbili. Kwabe sekutholakala ukuthi igwebu elomile le-amorphous elinezinhlangothi ezimbili libonisa i-PBG kuphela nge-polarization kagesi eguquguqukayo. Inkinga ukuthi kukhona ama-polarizations amabili kugwebu le-3D.
Naphezu kobunzima obungase bube khona, igwebu le-30D lingabhekwa njengento ethembisayo emkhakheni wezithombe, ngokusho kwabacwaningi. Kunesizathu salokhu: Imithetho ye-Plateau iqinisekisa ukuthi imiphetho yakha ama-vertices e-tetrahedral kuphela. Futhi lokhu kuhlanganisa okukhulu kwamanethiwekhi ezithombe. Isibonelo esimangalisayo salokhu idayimane eline-PBG engu-XNUMX%.
Igwebu linendawo ye-tetrahedral yezixhumanisi ze-diamond lattice, kodwa liyahluka ngokuthi linemiphetho egobile kanye nobude bebhondi obungalingani kancane. Kusele kuphela ukuthola ukuthi umehluko onjalo uthinta kanjani izakhiwo ze-photonic futhi ngezinga elingakanani.
Uma izimbambo zegwebu elomile le-17D zenziwe zajiya, kuyenzeka udale amanethiwekhi ezithombe (izithombe ezingezansi) ezibonisa aphinyiselwe ama-PBG ezithombe afika ku-XNUMX%, aqhathaniswa noma aphakeme kunalawo ezibonelo ezijwayelekile zamakristalu ezithombe azihlanganisele wona.
Isithombe #1: Amanethiwekhi egwebu lezithombe atholwe ngokujiya imiphetho yesakhiwo se-Ware-Phelan (kwesokunxele), isakhiwo se-Kelvin (maphakathi) kanye negwebu le-C15 (kwesokudla).
Ukuze usebenzise imodeli enjalo ngokusebenza, i-foam eyomile kufanele iqale icwecwe bese igcotshwa nge-dielectric material. Ngokwemvelo, i-PBG yegwebu izoba ngaphansi kunaleyo ye-photonic crystal, kodwa lokhu kungalungile kunganqotshwa ngenani lezinzuzo. Okokuqala, ukuzihlela kwegwebu kungase kuvumele ukukhiqizwa okusheshayo kwamasampula amakhulu. Okwesibili, i-photonic foam heterostructures, esekelwe ocwaningweni lwangaphambilini, ingaba nohlu olubanzi lwezinhlelo zokusebenza.
Imiphumela yocwaningo
Okokuqala, kwakudingeka ukutadisha igwebu elomile, elichazwa njenge-minima yendawo yesifunda esihlangene i-tessellation* ngaphansi kwemingcele yevolumu, ukuze ijometri yokugcina ilalele imithetho ye-Plateau.
I-Tessellation* - ukuhlukanisa indiza ibe izingxenye zezingxenye ezivala ngokuphelele indiza yonke ngaphandle kokushiya izikhala.
Ukwakha amagwebu e-Ware-Phelan, i-Kelvin, ne-C15, ososayensi baqale ngama-Voronoi anesisindo ama-tessellations we-BCC, A15, noma amakristalu e-C15, ngokulandelana.
Umdwebo we-Voronoi
Amapharamitha akhethwe ngendlela yokuthi wonke amaseli okuhlukanisa abe nevolumu efanayo.
Amanethiwekhi akhiwe kusukela emaphethelweni agobile amagwebu futhi kusukela emaphethelweni e-tessellation aqondile yabanduleli bawo ahlolisiswa. Ukuhlola i-topology yazo zonke izinhlobo zegwebu, izibalo zeringi*.
Izibalo ezikhalayo (izibalo ezikhalayo)*Ukuhlaziywa kwezici ze-topological zezinto zenethiwekhi (uketshezi, amasistimu ekristalu noma ama-amorphous) ngokuvamile kusekelwe kumbono wegrafu kusetshenziswa ama-node ama-athomu namabhondi okuxhumana kwe-interatomic. Ukungabikho noma ukuba khona kokuxhumana phakathi kwamanodi amabili kunqunywa ngokuhlaziya imisebenzi yokusatshalaliswa kwe-radial egcwele nengxenye yesistimu. Kokubalulekile kwenethiwekhi, ukulandelana kwamanodi nezixhumanisi ezixhunywe ochungechungeni ngaphandle kokugqagqana kubizwa ngokuthi umzila. Ukulandela le ncazelo, indandatho imane iyindlela evaliwe. Uma uhlola ngokucophelela i-node ethile yenethiwekhi, ungabona ukuthi le nodi ingabamba iqhaza emasongweni amaningi. Ngayinye yalezi ringi ibonakala ngobukhulu bayo futhi ingahlukaniswa ngokusekelwe ebudlelwaneni phakathi kwamanodi nezixhumanisi ezakhayo.
Indlela yokuqala yokuchaza indandatho yanikezwa uShirley W. King. Ukutadisha ukuxhumana kwe-SiO2 eyingilazi, uchaza indandatho njengendlela emfushane kakhulu phakathi komakhelwane ababili abaseduze benodi ethile.
Esimeni socwaningo olucutshungulwayo, izibalo zenziwe ngenani lamaringi amafushane kakhulu ku-vertex kuyunithi yeseli.
Iseli elilodwa kumodeli ye-Kelvin linezikwele ezingu-2 namaheksagoni angu-4 ku-vertex ngayinye, kodwa i-TCP (i-tetrahedral close-packed) igwebu inobuso obunezinhlangothi ezinezinhlangothi ezine kuphela (isilinganiso: 5.2 kanye no-0.78 kugwebu le-Ware-Phelan; 5.3 kanye no-0.71 kugwebu le-C15). I-Voronoi tessellations A15 ne-C15 yizakhiwo ze-TCP ezinenani elikhulu nelincane kakhulu lamaphethelo (f) ngeseli elingu-1. Ngakho-ke, isakhiwo se-Ware-Phelan sinenani elikhulu lobuso (f = 13 + 1/2), futhi i-C15 inombolo encane yobuso (f = 13 + 1/3).
Ngemva kokuqeda ukulungiswa kwethiyori, ososayensi baqala ukwenza imodeli yenethiwekhi ye-photonic esekelwe ezimbanjeni ezomile zegwebu, i.e. inethiwekhi ye-foam-photon. Kutholwe ukuthi ngenani le-PBG le-20% ukusebenza kwesistimu kukhuliswa, kodwa ku-15% igwebu le-Ware-Phelan liba nokungazinzi. Ngalesi sizathu, ososayensi abazange bacabangele igwebu elimanzi, lapho imingcele ye-Plateau inezingxenye ezinqamulayo ze-tricuspid. Kunalokho, kwakugxilwe ezakhiweni ezinogwebu ezomile, lapho ososayensi babengase bandise kancane kancane ukushuba kwezimbambo.
Ngaphezu kwalokho, unqenqema ngalunye luyi-eksisi ephakathi ye-spherocylinder (capsule), lapho i-radius iyipharamitha yokulungisa.
Abacwaningi basikhumbuza ukuthi amanethiwekhi anjalo amagwebu awawona amagwebu ngomqondo ongokoqobo, kodwa ukuze kube lula embikweni wabo azobizwa ngokuthi “igwebu” noma “inethiwekhi yegwebu.”
Ngesikhathi sokulingisa, ipharamitha yacatshangelwa ɛ (ukungafani kwe-dielectric) - ingxenye ye-dielectric constants yezinto ezinamavelu aphezulu futhi aphansi okushisa. Umehluko we-dielectric ucatshangwa ukuthi uphakathi kuka-13 no-1, ovame ukusetshenziswa ezincwadini njengezinga elijwayelekile uma kuqhathaniswa ukusebenza kwemiklamo ehlukahlukene ye-photonic.
Kunethiwekhi ngayinye, irediyasi yemiphetho (ama-spherocylinders) ilungiselelwe isilinganiso esiphezulu segebe lebhendi nendawo yalo: ∆ω/ωm, lapho ∆ω ububanzi bebhendi yefrikhwensi, futhi ωm - imvamisa ngaphakathi kwendawo.
Isithombe #2: Isakhiwo sendawo yesithombe segwebu le-Ware-Phelan (elibomvu), igwebu le-Kelvin (eliluhlaza okwesibhakabhaka), negwebu le-C15 (eliluhlaza).
Okulandelayo, osayizi be-PBG balinganiswa futhi kwatholakala ukuthi: 7.7% wegwebu le-Kelvin, u-13.0% wegwebu le-C15 kanye no-16.9% wegwebu le-Ware-Phelan. Ukunciphisa indawo kukhulisa usayizi we-PBG ngo-0.7%, 0.3 noma 1.3%.
Njengoba kwacaca ekuhlaziyweni, amanethiwekhi e-TCP anosayizi abakhulu kakhulu be-PBG kunamanethiwekhi kaKelvin. Kula manethiwekhi e-TCP amabili, igwebu le-Ware-Phelan linosayizi omkhulu we-bandgap, okungenzeka ukuthi kungenxa yoshintsho oluncane kubude besixhumanisi. Ososayensi bakholelwa ukuthi ukuhluka kobude bebhondi kungase kube isizathu esiyinhloko sokuthi kungani ohlelweni lwabo, i.e. kugwebu le-Ware-Phelan, i-PBG incane kunedayimane (31.6%) noma ohlelweni lweLaves (28.3%).
Isici esibaluleke ngokulinganayo kuma-photonics yi-isotropy ye-PBG, evumela ukudalwa kwamagagasi e-waveguides emumo ongaqondakali. Ama-Photonic quasicrystals, kanye namanethiwekhi e-amorphous photonic, angaphezulu kwe-isotropic kunamakristalu ezithombe zakudala.
Isakhiwo se-foam-photonic esingaphansi kocwaningo sinezinga eliphezulu le-isotropy. Ngezansi ifomula yokunquma i-anisotropy coefficient (okungukuthi, izinga lomehluko kuzakhiwo zendawo ethile) PBG (А):
A: = (√Var[ωHDB]+Var[ωI-LAB]) / ωm
Igwebu le-C15 litholakale line-anisotropy ephansi kakhulu (1.0%), lilandelwa igwebu le-Weir-Phelan (1.2%). Ngakho-ke, lezi zakhiwo ziyi-isotropic kakhulu.
Kodwa isakhiwo se-Kelvin sibonisa i-anisotropy coefficient engu-3.5%, esondelene kakhulu nesistimu yeLaves (3.4%) nedayimane (4.2%). Kodwa-ke, ngisho nalezi zinkomba azizona ezimbi kakhulu, ngoba kukhona nezinhlelo ze-cubic ezilula ezine-coefficient ye-anisotropy engu-8.8% kanye namanethiwekhi edayimane ane-hexagonal ane-9.7%.
Ngokwenza, lapho kudingekile ukufeza inani eliphakeme le-PBG, ngezinye izikhathi kuyadingeka ukushintsha imingcele ethile yomzimba yesakhiwo. Kulokhu, leli pharamitha liyi-radius yama-spherocylinders. Ososayensi benza izibalo zezibalo lapho banquma khona ubudlelwano phakathi kwegebe le-photonic band nobubanzi balo njengomsebenzi. ɛ. Ngevelu ngayinye etholiwe, irediyasi ithuthukiswe ukuze ikhule ∆ω/ωm.
Isithombe No. 3: ukuqhathaniswa kwe-∆ω/ωm yamanethiwekhi e-foam ahloliwe (C15, Kelvin, Weir-Phelan) nezinye izakhiwo (idayimane, idayimane eline-hexagonal, i-Laves, i-SC - i-cubic evamile).
Igwebu le-Weir-Phelan ligcina osayizi abamukelekile be-PBG abangu-8% ukuya kokungafani kwe-dielectric ɛ≈9, futhi irediyasi yanyuswa ukuze kuzuzwe inani eliphakeme le-PBG lika-15%. Ama-PBG ayanyamalala uma ɛ <6.5. Njengoba kulindelekile, isakhiwo sedayimane sine-PBG enkulu kunazo zonke phakathi kwazo zonke izakhiwo ezifundwayo.
Ukuze uthole ulwazi oluningiliziwe ngama-nuances ocwaningo, ngincoma ukubheka и kuyena.
Epilogue
Isisusa esiyinhloko sokwenza lolu cwaningo isifiso sokuphendula umbuzo wokuthi amanethiwekhi egwebu angabonisa yini i-PBG egcwele. Ukuguqula imiphetho yezakhiwo zegwebu ezomile zibe amanethiwekhi ezithombe kubonise ukuthi zingakwazi.
Okwamanje, i-foam ayisona isakhiwo esifundwe ngokukhethekile. Yiqiniso, kukhona izifundo ezinikeza imiphumela emihle mayelana namanethiwekhi we-amorphous, kodwa zenziwa ezintweni ezincane kakhulu. Ukuthi uhlelo luzoziphatha kanjani njengoba ubukhulu balo bukhuphuka akukacaci.
Ngokusho kwababhali balolu cwaningo, umsebenzi wabo uvula amathuba amaningi okusungulwa kwesikhathi esizayo. Igwebu livame kakhulu emvelweni futhi kulula ukulenza, okwenza lesi sakhiwo sithandeke kakhulu ekusebenzeni okusebenzayo.
Ososayensi babiza i-inthanethi ngesinye sezinhlelo zokusebenza ezifisa kakhulu zocwaningo lwabo. Njengoba abacwaningi ngokwabo besho, ukudlulisa idatha nge-fiber optical akuyona into entsha, kodwa ukukhanya kusaguqulwa kube ugesi lapho uya khona. Izinto ze-Photonic bandgap zingaqondisa ukukhanya ngokunembe kakhulu kunezintambo ezivamile ze-fiber optic futhi zingasebenza njengama-transistors abonakalayo enza izibalo kusetshenziswa ukukhanya.
Kungakhathaliseki ukuthi zinkulu kangakanani izinhlelo, usemkhulu umsebenzi okufanele wenziwe. Nokho, abukho ubunkimbinkimbi bokwenza ucwaningo noma ubunkimbinkimbi bokusebenzisa izivivinyo akukwazi ukunqoba umdlandla wososayensi nesifiso sabo sokuthuthukisa umhlaba wezobuchwepheshe.
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Source: www.habr.com